4.8.3 \(x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0\)

ODE
\[ x^6 \left (-y(x)^2\right )+x^3 y'(x)+(3-2 x) x^2 y(x)+3=0 \] ODE Classification

[_rational, _Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.0132444 (sec), leaf count = 25

\[\left \{\left \{y(x)\to \frac {\frac {1}{c_1 e^{4 x}+\frac {1}{4}}-3}{x^3}\right \}\right \}\]

Maple
cpu = 0.021 (sec), leaf count = 32

\[ \left \{ {\frac {1}{2}\ln \left ({\frac {2\,{x}^{3}y \relax (x ) }{3}}+2 \right ) }-{\frac {\ln \left (2\,{x}^{3}y \relax (x ) -2 \right ) }{2}}+2\,x+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[3 + (3 - 2*x)*x^2*y[x] - x^6*y[x]^2 + x^3*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-3 + (1/4 + E^(4*x)*C[1])^(-1))/x^3}}

Maple raw input

dsolve(x^3*diff(y(x),x)+3+(3-2*x)*x^2*y(x)-x^6*y(x)^2 = 0, y(x),'implicit')

Maple raw output

1/2*ln(2/3*x^3*y(x)+2)-1/2*ln(2*x^3*y(x)-2)+2*x+_C1 = 0